Quantum Tamo-Barg (QTB) code[1]
Description
A member of a family of Galois-qudit CSS codes whose underlying classical codes consist of Tamo-Barg codes together with specific low-weight codewords. Folded versions of QTB codes, or FQTB codes, defined on qudits whose dimension depends on \(n\), yield explicit examples of QLRCs of arbitrary locality \(r\) [1; Cor. 64].Protection
A family of QTBs can be defined for every prime \(r\), rate \(R\in(0,1)\), and qudit dimension \(q = n+1\) such that their relative distance is \(\delta \geq 1 - \sqrt{(1+R)/2} - O(1/r)\) [1; Thm. 62].
Folding these codes by combining qudits into larger qudits yields FQTB codes with relative distance \(\delta \geq (1-R)/2 - O(1/\sqrt{r})\) [1; Cor. 64] and qudit dimension \(q = n^{O(r^2)}\). This relative distance is of order \(O(1/\sqrt{r})\) below the Singleton-like QLRC bound.
Decoding
Polynomially efficient decoder for QTB codes against errors acting on a number of subsystems that can go up to half of the distance bound proved for the family [1; Thm. 69]. The decoder is based on decoding RS codes, and its runtime is independent of the locality \(r\).Polynomially efficient decoder for FQTB codes against errors acting on a number of subsystems that can go up to half of the distance bound proved for the family [1; Cor. 72]. The runtime depends on the locality \(r\).Cousin
- Tamo-Barg code— QTB codes are CSS codes constructed from Tamo-Barg codes.
Member of code lists
Primary Hierarchy
Parents
Folded quantum Tamo-Barg codes yield explicit QLRCs of arbitrary prime locality \(r\), rate at least \(R\), relative distance \(\delta \geq (1-R)/2 - O(1/\sqrt{r})\), and qudit dimension \(q = n^{O(r^2)}\) [1; Cor. 64].
Quantum Tamo-Barg (QTB) code
References
- [1]
- L. Golowich and V. Guruswami, “Quantum Locally Recoverable Codes”, (2023) arXiv:2311.08653
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-03-26)
Cite as:
“Quantum Tamo-Barg (QTB) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_tamo_barg, arXiv:2606.11484